Below, we've broken down the SAT® Math section into its 4 official domains: Algebra, Problem Solving and Data Analysis, Advanced Math, and Geometry and Trigonometry. Read on for each domain's examples, questions, strategies, and tricks.
Algebra
The SAT Algebra domain focuses on assessing your ability to analyze, fluently solve, and create linear equations and inequalities, as well as solve systems of equations using various techniques. Approximately 13-15 questions on the SAT Math section are derived from this domain.
Strategies to Ace Algebra Questions
The key to solving linear functions effectively is understanding what they represent. Start by drawing or annotating graphs, as they help visualize slopes, intercepts, and the intersection point of two lines — often the solution to a system of equations. If a graph isn't provided, try rewriting the equation in slope-intercept form to make plotting easier.
When faced with multi-step problems, slow down and work through each step carefully to avoid small mistakes. Practicing complex problems regularly can help you build confidence and reduce test-day anxiety. Be sure to show your work and proceed methodically.
It's also important to memorize essential formulas related to linear equations, absolute values, and graphing — this forms the core of your algebra toolbox. Lastly, try plugging the answer choices back into the equation for multiple-choice questions. This strategy can be especially useful for verifying solutions to tricky problems involving equations or inequalities.
Algebra examples
The solutions to which inequality are represented by the shaded region of the graph?
| A. y ≤ −2x − 4 | |
| B. y ≤ −4x − 2 | |
| C. y ≥ 2x − 4 | |
| D. y ≥ 4x − 2 |
Hint:
The graph of a linear inequality of the form y ≥ mx + b has shading above a boundary line.
The graph of a linear inequality of the form y ≤ mx + b has shading below a boundary line.
In the xy-plane, line p is parallel to the line represented by the equation y = −2x + 7. If line p passes through the points (0, 0) and (9, r), what is the value of r ?
Hint:
First determine the slope of a line parallel to line l
. Then use this slope and the given point to determine the y-intercept of line k.
y = - 3 / 2 x + 1
y = kx + 1
In the system of equations shown, k is a constant. If the system has infinitely many solutions, what is the value of k ?
Hint:
Each linear equation in the given system is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
Problem-Solving and Data Analysis
This category focuses on problems involving ratios, percentages, and 1- or 2-variable data. These questions often reference statistical terms (mean, median, mode), scatter plots, lines of best fit, data collection methods, and percent or ratio relationships. Box-and-whisker plot questions, when included, also fall under this domain. It typically accounts for 5-7 questions on the SAT Math section.
Strategies to Ace Problem-Solving and Data Analysis Questions
As you prepare for this section, ensure you understand the key technical terms' definitions and know how to calculate values or interpret data sets. SAT Math questions in this domain often include incorrect answer choices based on common mistakes or misconceptions. For instance, if a question asks for the mean of a dataset, one of the answer choices may be the median. Mastering the relevant vocabulary will help you approach these questions with greater confidence and fewer distractions.
Another common challenge is that data points may be presented out of order. This can be especially important when calculating values like the median, where numerical order matters. Taking a few seconds to reorder the values can help you avoid simple but costly errors.
Problem-Solving and Data Analysis examples
The population of a certain town decreased by 4% from 2005 to 2015. If the population in 2015 is k times the population in 2005, what is the value of k ?
To decrease a value by p%, multiply it by ( 1 - p / 100 )
24, 25, 27, 28, 31, 32, 38
The data set shown represents the overall diameters, in inches, of 7 different sizes of tires sold by an auto shop. The tire size with a diameter of 38 inches was recorded incorrectly. If the diameter of 38 inches is removed from the data set, which statement best describes the effect on the mean and median diameters of the 7 tire sizes?
| A. Both the mean and the median will increase. | |
| B. Both the mean and the median will decrease. | |
| C. The mean will increase, and the median will decrease. | |
| D. The mean will decrease, and the median will increase. |
Hint:
Notice that the removed value of 38 is greater than all the values in the original data set.
The median of a data set with an odd number of values is the middle value, and the median of a data set with an even number of values is the average of the middle two values.
A set designer is painting a backdrop for a play at a rate of 18 square inches per minute. At what rate, in square feet per hour, is the set designer painting? (1 foot = 12 inches)
Hint:
First use the given unit conversion 1 foot = 12 inches to find a conversion for square inches and square feet.
Advanced Math
This domain covers a broad range of topics that go beyond basic algebra and extend into Algebra II, with some overlap into precalculus depending on your coursework. It includes nonlinear functions, expressions, and equations such as quadratics, exponential and square root functions, and systems of equations with 2 or more variables. You can recognize these questions by references to quadratics in various forms, expressions with exponents or roots, and function notation, especially composite functions (e.g., g(f(x))). This domain typically accounts for 13-15 questions on the SAT Math section.
Strategies to Ace Advanced Math Questions
This category primarily focuses on higher-order functions and expressions, so familiarize yourself with manipulating the different expressions you will encounter. For instance, solving or rewriting quadratic functions using techniques such as factoring and completing the square, and the quadratic formula will significantly enhance your comfort and consistency with these questions. Similarly, it's beneficial to understand how to rewrite exponents and roots in terms of each other, as this can simplify and make many equivalent expression questions easier.
Advanced Math examples
In the xy-plane, a line with equation 4y = c for some constant c intersects the parabola y = 4x2 − 5x at exactly one point. What is the value of c?
Hint:
Intersection points (x, y) on the graph of a system of equations correspond to solutions to the system.
Which of the following quadratic equations has no real solutions?
| A. x2 − 12x + 36 = 0 | |
| B. x2 + 12x − 36 = 0 | |
| C. 10x2 − 12x + 36 = 0 | |
| D. 10x2 − 12x − 36 = 0 |
Hint:
A quadratic equation in one variable has 0, 1, or 2 solutions.
The function f is defined by f(x) = (x + 6)(x + 2)(x − 5), and the function g is defined by g(x) = f(x − 3). The graph of y = g(x) in the xy-plane has x-intercepts at (a, 0), (b, 0), and (c, 0), where a, b, and c are distinct constants. What is the value of abc ?
Hint:
The function g(x) = f(x − 3) is defined in terms of f(x), so g represents a horizontal shift to the function f.
Geometry and Trigonometry
The Geometry and Trigonometry domain of the SAT Math section assesses your ability to solve problems involving area and volume formulas, lines, angles, triangles, right triangles, trigonometry, and circles. This domain typically accounts for 5-7 questions on the SAT Math section.
Strategies to Ace Geometry and Trigonometry
Since geometry and trigonometry are the focus of this domain, a solid understanding of geometric rules, theorems, and basic trigonometric concepts is essential. Be sure you can identify how angles relate to each other within parallel lines and triangles, especially which angles are congruent (equal) or supplementary (adding up to 180 degrees). Circle theorems make up a smaller portion of this section and may not appear on every exam. However, it's still important to understand how to determine the angles and dimensions of a circle. Once you're confident with the other topics, spend time reviewing these concepts to ensure you're fully prepared.
Geometry and Trigonometry in Math examples
What is the length of side in right triangle ABC above?
| A. 2 | |
| B. 2√3 | |
| C. 4 | |
| D. 4√3 |
Hint:
Triangle ABC is a 30°-60°-90° triangle.
Triangles ABC and DEF are similar, where A corresponds to D, B corresponds to E, and C corresponds to F. If the measure of angle C is 58°, what is the measure, in degrees, of angle E?
Hint:
Corresponding angles of similar triangles are congruent.
In the given triangle, PQ = QR. What is the value of x ?
Hint:
An isosceles triangle has two sides that are congruent (equal in length) and a third side called the base.
How To Fill Student-Produced Responses (SPRs) on SAT Math
While most SAT Math questions are multiple-choice, some require generating and entering your own answer. These are called student-produced responses (SPRs). Instead of selecting from given options, you'll type your answer directly into the test platform. SPRs assess your ability to solve problems independently, without the structure or cues that come with multiple-choice questions. Some of these questions may have more than one correct answer, but you are required to submit only one.
To understand all the math topics tested on the SAT, take a look at our full SAT study guide. It breaks down each concept clearly and is a great place to start your prep.
Frequently Asked Questions (FAQs)
Algebra and Advanced Math each account for approximately 13–15 questions. As a result, the most common SAT Math question types include linear functions, inequalities, nonlinear equations, and nonlinear functions.
Most SAT Math mistakes are caused by stress, unfamiliarity with problem types, or poor time management. The best way to avoid these errors is by practicing with realistic questions at varying difficulty levels. For targeted practice by topic, try our SAT question bank.
Keep in mind that every question carries equal weight. First, focus on solving the questions you’re most confident in. Once you’ve worked through the easier questions, return to the tougher ones with a clearer mindset.
Many math questions can be solved efficiently using specific strategies and formulas. Review solution explanations — like those in our SAT Course — for examples of when and how to apply them, also, practice using the built-in digital calculator to become familiar with its functions.
References
- College Board. (2024). Algebra. SAT Suite of Assessments. Retrieved April 14, 2025, from https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types/algebra
- College Board. (2024). Problem-Solving and Data Analysis. SAT Suite of Assessments. Retrieved April 14, 2025, from https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types/problem-solving-data-analysis
- College Board. (2024). Advanced Math. SAT Suite of Assessments. Retrieved April 14, 2025, from https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types/advanced-math
- College Board. (2024). Geometry and Trigonometry. SAT Suite of Assessments. Retrieved April 14, 2025, from https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types/geometry-trigonometry
- College Board. (2024). Math on the SAT. SAT Suite of Assessments. Retrieved April 14, 2025, from https://satsuite.collegeboard.org/sat/whats-on-the-test/math
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